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Optimal Control of a PDE Model of an Invasive Species in a River

Author

Listed:
  • Rebecca Pettit

    (Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, USA)

  • Suzanne Lenhart

    (Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, USA)

Abstract

Managing invasive species in rivers can be assisted by appropriate adjustment of flow rates. Using a partial differential equation (PDE) model representing an invasive population in a river, we investigate controlling the water discharge rate as a management strategy. Our goal is to see how controlling the water discharge rate will affect the invasive population, and more specifically how water discharges may force the invasive population downstream. We complete the analysis of a flow control problem, which seeks to minimize the invasive population upstream while minimizing the cost of this management. Using an optimality system, consisting of our population PDE, an adjoint PDE, and corresponding optimal control characterization, we illustrate some numerical simulations in which parameters are varied to determine how far upstream the invasive population reaches. We also change the river’s cross-sectional area to investigate its impact on the optimal control.

Suggested Citation

  • Rebecca Pettit & Suzanne Lenhart, 2019. "Optimal Control of a PDE Model of an Invasive Species in a River," Mathematics, MDPI, vol. 7(10), pages 1-17, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:975-:d:276655
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    References listed on IDEAS

    as
    1. Gagnon, Karine & Peacock, Stephanie J. & Jin, Yu & Lewis, Mark A., 2015. "Modelling the spread of the invasive alga Codium fragile driven by long-distance dispersal of buoyant propagules," Ecological Modelling, Elsevier, vol. 316(C), pages 111-121.
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